Functional connectivity MRI (fcMRI) based on the blood oxygen level dependent (BOLD) contrast has become a widely used modality for mapping the brain's functional architecture. In recent years, applications of fcMRI have led to numerous breakthroughs in both clinical research and basic sciences. However, there are a number of unresolved issues associated with fcMRI relating to both the modality itself, and to methods used to analyse fcMRI data. The aim of this thesis was twofold: to develop novel data analysis procedures, and to demonstrate their feasibility in dedicated neuroimaging studies. Subject head movement can act as a significant confound in fcMRI. Investigating this issue, it was found that subject motion can induce significant increases and decreases in functional connectivity across the brain. A novel motion correction method was developed, which proved more effective than standard procedures in the removal of motion induced connectivity changes. The BOLD contrast is not a direct measure of neural activity, it measures the hemodynamic response caused by changes in neural activity, which varies across the brain. The hypercapnic state is often used to calibrate the BOLD signal. This calibration crucially relies on the assumption that hypercapnia does not affect neuronal activity. An investigation into the hypercapnic state revealed that it is associated with both increases and decreases in functional connectivity. Whilst carrying out this investigation, a number of limitations, such as the need for a hypothesis and information loss, were identified in standard data analysis procedures. Three novel methods were developed to address these limitations. The efficacy of these methods was demonstrated in four different neuroimaging studies, which investigated functional connectivity changes induced by hypercapnia, aerobic exercise, hormonal changes across the menstrual cycle, and electroconvulsive therapy treatment in depression.